Currency failure generally occurs due to the type of hyperinflation, and there is always the potential for technical failure, currency competition, political issues and so on. As the main basic rule, there is no currency that can be considered very safe from failure and difficult times. so is it possible that bitcoin can become worthless?
On the real note, currency failure occurs when people begin to lose faith and stop believing in it. It is when the patronage of such coins by investors and traders on the market ceases and because each coin is largely influenced by the principle of supply and demand, lack of demand means no price/value for the coin on the market.
Bitcoin has the largest market cap thus with the largest demand on the market. Before considering Bitcoin becoming worthless, first consider other coins becoming worthless because Bitcoin has become a standard of measure for the value of most of the coins on the market.